8th Grade Systems of Equations Test Prep Questions

📚 Quick Study Guide

• 🍎 A system of equations is a set of two or more equations containing two or more variables.
• 🔢 The solution to a system of equations is the set of values that satisfy all equations in the system simultaneously.
• 📈 Graphing: Graph each equation and find the point(s) of intersection. This method is best for simple equations.
• ➕ Substitution: Solve one equation for one variable and substitute that expression into the other equation.
• ➖ Elimination: Add or subtract the equations to eliminate one variable. Sometimes you need to multiply one or both equations by a constant first.
• 💡 When solving, if you get a true statement (e.g., $0 = 0$), the system has infinitely many solutions. If you get a false statement (e.g., $0 = 1$), the system has no solution.
• ✍️ Remember to check your solution by plugging the values back into the original equations!

🧪 Practice Quiz

1. What is the solution to the following system of equations? $y = x + 1$ $y = 2x - 1$
   1. (2, 3)
   2. (3, 2)
   3. (2, 1)
   4. (1, 2)
2. Solve the system of equations using substitution: $x + y = 5$ $x = y - 1$
   1. (3, 2)
   2. (2, 3)
   3. (4, 1)
   4. (1, 4)
3. Solve the system of equations using elimination: $2x + y = 7$ $x - y = 2$
   1. (3, 1)
   2. (1, 3)
   3. (3, 2)
   4. (2, 3)
4. Which of the following systems of equations has no solution?
   1. $y = x + 1$, $y = x + 2$
   2. $y = x + 1$, $y = 2x + 1$
   3. $y = x + 1$, $y = -x + 1$
   4. $y = 2x + 1$, $y = 2x + 2$
5. Which of the following systems of equations has infinitely many solutions?
   1. $y = x + 1$, $y = x + 1$
   2. $y = x + 1$, $y = x + 2$
   3. $y = x + 1$, $y = -x + 1$
   4. $y = 2x + 1$, $y = 2x + 2$
6. What is the value of $x$ in the solution to the following system? $3x + 2y = 8$ $x + y = 3$
   1. 2
   2. -2
   3. 3
   4. -3
7. Solve for $y$: $4x - 3y = 10$ $x + y = 1$
   1. -2
   2. 2
   3. -3
   4. 3